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Characterizing Quadratic Convection and Electromagnetically Induced Flow of Couple Stress Fluids in Microchannels

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Abstract

This paper investigates the effects of quadratic convection on the electro-magneto-hydrodynamically driven flow of couple stress fluid in a microchannel. The integration of quadratic convection effects and electro-magnetic hydrodynamics in microchannels offers high potential for advancing microfluidic technologies and opening new avenues of innovation. In microfluidic systems, the couple stress fluids describe more accurately the flow mechanisms. The current mathematical modeling offers more details on the impacts of viscous dissipation and joule heating. Analytical series solutions for the temperature and velocity profiles are used with a homotopy perturbation technique. The impacts of all the parameters are explored using tables and graphs. The dynamics of velocity and temperature distribution are analyzed in detail. Furthermore, the Nusselt number values are computed and shown using funnel charts. From the graphical results it is concluded that the simultaneous impact of quadratic convection and thermal Grashof number enhances the entire velocity profile over the whole channel. The velocity and temperature profile are also observed to increase with increasing Brinkman number. The thermal profile is considerably increased by the Hartmann number, the Grashof number, and the quadratic convection parameter. The thermal profile always has a peak near the center of the channel. The thermal profile is reduced by the couple stress fluid variable parameter. The present study can be of assistance to novel advancements in various fields such as lab-on-a-chip devices, chemical synthesis, and thermal management.

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Abbreviations

\(\underline{u}\) :

Velocity vector

\(\underline{X},\underline{Y},\underline{Z}\) :

Cartesian coordinate system

\(\lambda ,\mu \) :

Coefficients of viscosity

\({\varvec{c}}\) :

Body couple per unit mass

\(\eta \) :

Coefficient of couple stress viscosity

\(\underline{p}\) :

Pressure

\(g\) :

Gravity

\({\beta }_{l},{\beta }_{n}\) :

Thermal and quadratic expansion coefficients

\(\underline{T}\) :

Temperature

\(\rho \) :

Density

\(t{\prime}\) :

Time

F:

Body force

\(\kappa \) :

Thermal conductivity

\({h}_{c}\) :

Specific heat capacity

\({h}_{f}\) :

Heat flux vector

\(\sigma \) :

Electrical conductivity

\(\overrightarrow{\mathrm{E}}\) :

Electrical field

\(\nu \) :

Kinematic viscosity

\(\gamma \) :

Hartmann number

\({\xi }_{e}\) :

Electrical strength

\({\xi }_{c}\) :

Couple stress fluid parameter

\({\xi }_{1}\) :

Thermal Grashof number

\({\xi }_{2}\) :

Quadratic thermal convection parameter

\(\Omega \) :

Pressure gradient parameter

\(\beta \) :

Brinkman number

\({\zeta }_{1}\) :

Heat generation impact

\({\zeta }_{2}\) :

Ratio between heat conduction and Joule heating

\({D}_{h}\) :

Hydraulic diameter

\(N\) :

Nusselt number

\(\varepsilon \) :

Embedded parameter

\(\mathop{L}\limits^{\leftrightarrow} _{u} ,\mathop{L}\limits^{\leftrightarrow} _{T}\) :

Linear operator

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Funding

Lijun Zhang and M. M. Bhatti are supported by the National Natural Science Foundation of China No. 12172199.

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Authors and Affiliations

  1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, Shandong, China

    Lijun Zhang & M. M. Bhatti

  2. Material Science Innovation and Modelling (MaSIM) Research Focus Area, North-West University (Mafikeng Campus), Private Bag X2046, Mmabatho, 2735, South Africa

    Lijun Zhang & M. M. Bhatti

  3. Department of Engineering, TCU, Fort Worth, TX, USA

    Efstathios E. Michaelides

  4. Department of Mathematics and Statistics, International Islamic University, Islamabad, 44000, Pakistan

    R. Ellahi

  5. Center for Modeling and Computer Simulation, Research Institute, King Fahd University of Petroleum and Minerals, 31261, Dhahran, Saudi Arabia

    R. Ellahi

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Contributions

M. M. Bhatti, and Lijun Zhang, provided the concept and edited the draft of manuscript. Lijun Zhang and Efstathios E. Michaelides conducted the literature review and wrote the first draft of the manuscript. Efstathios E. Michaelides and R. Ellahi edited the draft of the manuscript.

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Correspondence to M. M. Bhatti.

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Zhang, L., Bhatti, M.M., Michaelides, E.E. et al. Characterizing Quadratic Convection and Electromagnetically Induced Flow of Couple Stress Fluids in Microchannels. Qual. Theory Dyn. Syst. 23, 35 (2024). https://doi.org/10.1007/s12346-023-00883-z

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